Question

A jar contains 8 black and 2 red marbles. Marbles are drawn with re-

placement until a red one is found.

(a) Write down an expression representing the probability that it will

take k drawings.

(b) How many drawings would you expect to make?

4. In the setup of the previous problem, if 3 marbles are drawn without

replacement, what is the expected number of red marbles removed?

Answer 1

a)We are drawing with replacement. Hence to get a red marble in kth drawing, we need to get black in first (k-1) drawings

subtracting the two equations

4)In one draw-> Prob=2/10

Second draw=(8/10)*(2/9)

third draw->(8/10)*(7/9)*(2/8)

From fourth draw, there is replacement, which means overall we would have 7 balls